Four Super Bowl wins is a great achievement. And although Brady scored a come-from-behind touchdown to put the Patriots up in Super Bowl XLIX, the Seahawks still had time to win the game. And what happened when Brady was sitting on the bench, would turn the tables. Another Seattle miracle looked like it was going to happen, when Jermaine Kearse caught a bouncing ball on his back on the 5-yard line with time to run a few plays. After Marshawn Lynch got the ball down to the 1-yard line, it looked like the Seahawks would finish off the day with a win. And then, Russell Wilson’s pass from the 1-yard line was snagged by the Patriots Malcom Butler at the goal lone. Disbelief! There was still enough time to see yet another turn of events when Brady was going to have to dig himself out of the end zone when taking the center from the 1-yard line, but the Seahawks jumped offside at the line and the penalty gave the Patriots enough room to manuever.
It was Belichick's fourth Super Bowl Championship and it puts him on the top of the list, right? Not exactly! You see, the Super Bowl era is approaching 50 years, but the NFL capped off the 1966 season with the first Super Bowl between the Green Bay Packers and the Kansas City Chiefs. There was an NFL Champion from 1920 through the 1965 season to consider as well. Vince Lombardi won 5 NFL Championships, although only two were capped off by Super Bowls. In addition to Chuck Noll's four Super Bowl wins, Guy Chamberlin won 4 NFL Championships in 5 years, Curly Lambeau won 6, and George Halas won 6 over the decades he coached.
If you want to come up with extra reasons that Bellichick's championships should count more because they are in the modern era, you might want to consider a few circumstances that Bellichick did not have to deal with in the modern era. Lambeau's Packers were cash strapped during his era and stock sales bailed them out. Halas was only not struggling to keep the Bears solvent, he was constantly working to keep the league running. And his Bears were also playing during the Depression and World War II. During the war, Halas entered the service and missed a few opportunities to coach the Bears to Championships, but the Bears had won 7 overall championships in the first 27 seasons.
Chamberlin was a pretty special guy too. His best player in most of his championship years was Chamberlin himself. He was very fast and played end on both defense and offense.
And there is one other coach who might get a lot of votes himself as someone who deserves to be among the greatest, Paul Brown. Brown "only" won 3 NFL Championships, but he won 4 AAFC championships before his Browns came into the NFL.
Belichick is among the top coaches in history, but it's hard to say his the best. For more on the greatest coaches in NFL history, see Pillars of the NFL: Coaches Who Have Won Three or More Championships.